Matt G.

asked • 02/12/14

parabolas, ellipses and hyperbolas can someone give me three conic sections.indiciate mathematical features of the conic corresponds within the examples.

conic sections - parabolas, ellipses and hyperbolas.  Look around in your day (home, work, etc) and see if you observe any of the conic sections.  In each explanation, indiciate what one of the mathematical features of the conic (vertex, foci, etc) corresponds with in your examples.
 
 
2 examples would be a big help. having trouble with this part especially -->In each explanation, indiciate what one of the mathematical features of the conic (vertex, foci, etc) corresponds with in your examples.

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Steve S. answered • 02/12/14

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Thrown baseball: path is a parabola with vertex the highest point.
 
Looking at the rim of a circular plate in the center of a table you're sitting at: ellipse whose major axis is the diameter of the circle.
 
The shadows on a wall caused by a household lamp: hyperbola
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Matt G.

I understand the concept of what creates or the shape of something making a conic shape the part I don't know how to explain is the  mathematical part.  ------>  In each explanation, indiciate what one of the mathematical features of the conic (vertex, foci, etc) corresponds with in your examples. What Mathematical feature of each of your examples of the conic correspond with? Or am I just making this harder and over thinking it? Maybe its just giving the examples and the specific Conic shape. I just assumed it had to have some Mathematical equations to it or something more. I guess an example might be the shadows caused by a household lamp represent a hyperbola which is represented by (y-k)squared over A squared -(x-h)squared over B squared =1 or (x-h)squared over A squared -(y-k)squared over B squared =1. Does that sound right or am I overthinking it and don't need to put the equations in there??? suggestions appreciated
 
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02/12/14

Steve S.

Perhaps you are making it too hard.
 
As a teacher I'd accept my answer for the parabola example.
 
I might add the following to the ellipse example: the ellipse's minor axis is the circle's diameter foreshortened by perspective.
 
For the hyperbola you could say the vertices lie on the intersection line of a plane that is perpendicular to the wall and floor and contains the light bulb filament.
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02/13/14

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